Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 130-134). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--Rutgers University, 2010. / "Graduate Program in Computer Science." Includes bibliographical references (p. 62-64).

Thesis (M.S.)--Marquette University, 2009. / Edwin Yaz, Susan Schneider, Peter Schmidt, Advisors.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2003. / Includes bibliographical references. Also available on the Internet.

Thesis (M.S.)--University of Wisconsin--Madison. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 259-264).

No description available.

In an age where computers challenge the smartest human beings in cognitive tasks, the conspicuous discrepancy between robot and animal locomotion appears paradoxical. While animals can move around autonomously in complex environments, today’s robots struggle to independently operate in such surroundings. There are many reasons for robots’ inferior performance, but arguably the most important one is our missing understanding of complexity. This thesis introduces the notion of discrete actuation for the study of locomotion in robots and animals. The actuation of a system with discrete actuation is restricted to be applied at a finite number of instants in time and is impulsive. We find that, despite their simplicity, such systems can predict various experimental observations and inspire novel technologies for robot design and control. We further find that, through the study of discrete actuation, causal relationships between actuation and resulting behaviour are revealed and become quantifiable, which relates the findings presented in this thesis to the broader concepts of complexity, self-organisation, and self-stability. We present four case studies in Chapters 3-6 which demonstrate how the concept of discrete actuation can be employed to understand the physics of locomotion and to facilitate novel robot technologies. We first introduce the impulsive eccentric wheel model which is a discretely actuated system for the study of hopping locomotion. We find that the model predicts robot hopping trajectories and animal related hopping characteristics by reducing the dynamics of hopping–usually described by hybrid differential equations–to analytic maps. The reduction of complexity of the model equations reveals the underlying physics of the locomotion process, and we identify the importance of robot shape and mass distribution for the locomotion performance. As a concrete application of the model, we compare the energetics of hopping and rolling locomotion in environments with obstacles and find when it is better to hop than to roll, based on the fundamental physical principles we discover in the model analysis. The theoretical insights of this modelling approach enable new actuation techniques and design for robots which we display in Robbit; a robot that uses strictly convex foot shapes and rotational impulses to induce hopping locomotion. We show that such systems outperform hopping with non-strictly convex shapes in terms of energy effective and robust locomotion. A system with discrete actuation motivates the exploitation of shape and the environment to improve locomotion dynamics, which reveals advantageous effect of inelastic impacts between the robot foot and the environment. We support this idea with experimental results from the robot CaneBot which can change its foot shape to induce timed impacts with the environment. Even though inelastic impacts are commonly considered detrimental for locomotion dynamics, we show that their appropriate control improves the locomotion speed considerably. The findings presented in this thesis show that discrete actuation for locomotion inspires novel ways to appreciate locomotion dynamics and facilitates unique control and design technologies for robots. Furthermore, discrete actuation emphasises the definition of causality in complex systems which we believe will bring robots closer to the locomotion behaviour of animals, enabling more agile and energy effective robots.

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Electrical impedance tomography (EIT) is an imaging modality with many possible practical applications. It is mainly used for geophysical applications, for which it is called electrical resistivity tomography. There have also been many proposed medical applications such as respiratory monitoring and breast tumour screening. Although there have been many uniqueness and stability results published over the last few decades, most of the results are in the context of the theoretical continuous problem. In practice however, we almost always have to solve a discretised problem for which very few theoretical results exist. In this thesis we aim to bridge the gap between the continuous and discrete problems. The first problem we solve is the three-dimensional triangulation problem of uniquely embedding a tetrahedral mesh in R3. We parameterise the problem in terms of dihedral angles and we provide a constructive procedure for identifying the independent angles and the independent set of constraints that the dependent angles must satisfy. We then use the implicit function theorem to prove that the embedding is locally unique. We also present a numerical example to illustrate that the result works in practice. Without the understanding of the geometric constraints involved in embedding a three-dimensional triangulation, we cannot solve more complex problems involving embeddings of finite element meshes. We next investigate the discrete EIT problem for anisotropic conductivity. It is well known that the entries of the finite element system matrix for piecewise linear potential and piecewise constant conductivity are equivalent to conductance values of resistors defined on the edges of the finite element mesh. We attempt to tackle the problem of embedding a finite element mesh in R3, such that it is consistent with some known edge conductance values. It is a well known result that for the anisotropic conductivity problem, the boundary data is invariant under diffeomorphisms that fix the boundary. Before investigating this effect on the discrete case, we define the linear map from conductivities to edge conductances and investigate the injectivity of this map for a simplistic example. This provides an illustrative example of how a poor choice of finite element mesh can result in a non-unique solution to the discrete inverse problem of EIT. We then extend the investigation to finding interior vertex positions and conductivity distributions that are consistent with the known edge conductances. The results show that if the total number of interior vertex coordinates and anisotropic conductivity variables is larger than the number of edges in the mesh, then there exist discrete diffeomorphisms that perturb the vertices and conductivities such that no change in the edge conductances is observed. We also show that the non-uniqueness caused by the non-injectivity of the linear map has a larger effect than the non-uniqueness caused by diffeomorphism invariance.

The theoretical properties of the Maximum Likelihood estimator, for both single input-single output and multivariable systems, are considered. New results relative to convergence properties of some identification methods of single input-single output systems are obtained. A unified approach to the Maximum Likelihood identification method of multivariable systems is proposed. Numerical tests on a computer are performed. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate